Dan Hibiki from the Street Fighter games. While his father Go was a great fighter, Dan himself is widely considered to be the weakest character (storyline-wise—also objectively gameplay-wise) in the series, and yet he still thinks of himself as the greatest fighter who ever lived. He's actually so weak that when Demitri Maximoff (a vampire) offers to make Dan into one of his servants, he takes back the offer after noting how low Dan's strength is compared to everybody else he's met. Dan himself is very insulted. ("Only the strong and beautiful can serve me. You fail on BOTH counts!")
Certain media shifts this a bit. In the manga Sakura Ganbaru!, he's not an elite fighter, but enough of one to make a living, and perceptive enough to remain a mentor to Sakura, as well as call Ken out on his injuries after the latter (barely) won against Sakura.
Then again, in the Sakuracomic mini-series by UDON, she agrees to study under Dan Hibiki only because "There's something to be learned from every fighter... even the bad ones!" Dan, of course, is utterly oblivious to this.
In Pocket Fighter, Dan is made to look even more weak. (Keep in mind that this is a game with Super-Deformed characters that runs on Rule of Funny.) His introduction begins with, "Upon deciding he was the strongest fighter in the world...", and in his ending, he gets harshly criticised by his own student. To quote, "All of your moves look retarded in addition to being completely useless in battle!"
Rufus of Street Fighter IV is fairly similar to Dan. He's very full of himself and believes he is the best fighter in America. The other characters constantly remind him of how he's too fat or his fighting style is too flashy for him to be a serious fighter. Gameplay-wise, though, he's an above-average character.
Although Ryu does point out in his after battle quote "your style has some serious potential, but your moves are too flashy," so Rufus' in game abilities were apparently not lost on the designers. On the other hand, outside of dating, he's shown to be very kind and aware of his lover's feelings, and fighting he really does have an overblown ego.
Waluigi from the Super Mario Bros. series, certainly qualifies. He thinks he's the greatest and that "everybody cheats but him." The Mushroom people absolutely loathe his being. The toads are usually scared or repulsed by him, and the Mario cast tends to ignore or hate him. This overlaps with Big Ego, Hidden Depths, however. Since he is an even worse Butt-Monkey than Luigi who failed to earn the respect (from the Mushroom Kingdom) and love (from Daisy) he wanted. Waluigi believes that the good things that should be happening to him are happening to everyone else. He hates everyone because of this, including himself.
One recurring NPC in Final Fantasy Tactics A2, the editor of the Bonga Bugle magazine (suggested to be more of a tabloid, really, but who's counting) lives and breathes this trope. It's surprising the localization team didn't name him some variation of the name.
Subverted with Kefka in Final Fantasy VI, who at first seems like an egotistical Harmless Villain who fits this trope. He would subvert it when he becomes a Monster Clown by poisoning an entire castle. For much of the first leg of the game, he seems to be a villain who still fits this trope as the half-mad ego-maniacal supporter of the supposed Big Bad. Players were itching to really dish out a good bit of karmic justice to him in the Disc One Final Dungeon. Then he subverts it again when he goes From Nobody to Nightmare, prompting the second half of the game where he is the ultimate adversary.
Mao from Disgaea 3: Absence of Justice constantly boasts about his brilliance and 1.8 million "E.Q.", but as Almaz points out, his calculations are never correct. He also assumes he is far more respected and admired by the other students than is actually the case. And the game would be over in half the time if he could just admit that he needs the help of others, and that his friends are more than just servants he allows to tag along with him.
Persona 4 has Teddie, who despite being an empty bear suit, thinks that he's the world's most suave ladies man. He gets a Bishōnen human form later on, and sadly for the other characters, his charms work on most non-story-related ladies.
Persona 3's Junpei Iori, who thinks of himself as an action hero and ladies' man, and flaunts himself as such to anyone who will listen (or anyone who doesn't immediately berate him for it, that is). Most infamously during the Beach Episode, where his success with women is taken down a peg or ten (granted, Akihiko and the Protagonist don't manage to get anyone either), and he quickly becomes The Resenter when the much more efficient and unassuming Main Character proves himself the real hero. Much of his character arc is about him growing out of this.
In Persona 5, Yuuki Mishima becomes this during his Confidant; his self-confidence was non-existent prior to creating the Phansite, but the power of managing the site quickly goes to his head, to the point that he's able to convince himself that he's responsible for the Phantoms' success. Luckily, the Protagonist is able to talk sense back into Yuuki before it gets too out of hand.
Several of the girls of Touhou are legends in their own minds:
Cirno, Touhou's resident ditz, proclaims herself to be the strongest and the smartest in Gensokyo. In reality, she's probably just the strongest and smartest fairy, and unfortunately for her, fairies in the Touhouverse are essentially mooks. Her name and number are practically synonymous with Baka.
Though the possibility of a subversion is creeping in with evidence her boast aren't quite as disproportionate as they seem. In Phantasmagoia of Flower View, Shikieki says she has "too much" power for a fairy, and in Great Fairy Warsshe forces Bonus Boss Marisa to go all-out with her "fairy extermination spells" to beat her, though she apparently comes off second-best despite technically winning the danmaku brawl.
Mima of the very first Touhou game, Highly Responsive to Prayers is quite powerful, but nowhere near as strong as she says she is.
She is the final boss of Story of Eastern Wonderland and the aforementioned Marisa was her minion in that game. It's pretty safe to say Mima is probably every bit as powerful as she claims she is.
Mystia isn't as featured as Cirno, but she does have her moments. Enough to make Alice say, "Mpf. Enough chirping, you windbag."
Nazrin's profile in Symposium of Post-Mysticism describes her as this. Despite being a small and easily intimidated mouse familiar, she has a huge ego that dwarfs her frame, mostly thanks to being pals with Bishamonten.
Todd "Maniac" Marshall, from the Wing Commander series, though the official Strategy Guide for Wing Commander Prophecy notes in Maniac's bio that he has the 14th highest kill score from the Kilrathi War (behind Blair's 11th), so there's evidence he isn't totally an unskilled braggart, at least in the cockpit. Romantic pursuits, however, are another issue entirely...
It would probably be far lower if he didn't live up to his callsign. A new player might be forgiven for wondering whether his AI functioned correctly...
Barry Dejay of the Backyard Sports series. He claims he can be the best at sports even with a broken ankle and a promotion to announcer.
Also, the fictional Barry Bonds. But he admits that he has a huge ego.
Don't forget Tony. He goes to town with this trope.
In Mass Effect, Conrad Verner seems to think that he's just as badass as Commander Shepard. In the first game, he tries to convince Shepard to make him a Spectre. One of Shepard's responses? "Conrad, I haven't been shot in the head nearly enough times to make that seem like a good idea." In the second, he appears (wearing a replica of Shepard's N7 armor) at a bar, trying to shut it down because a corrupt weapons merchant convinced him the bartender was selling red sand... which, even if she had been, it wouldn't matter, because red sand is completely legal on that planet. Two of Shepard's possible three responses involve causing bodily harm to him. (And if Shepard is female, he comes across as a sort of Stalker With a Crush.) He at one point literally tells Shepard to "sit back and watch how it's done." Shepard was pretty much giving him/herself an implied Face Palm for that entire conversation.
In Mass Effect 3, this definitely describes Kai Leng. While he is certainly a legitimate threat, he's not as dangerous as he would like to think he is and his over-inflated sense of pride leads to him woefullyunderestimating Shepard at several points throughout the game.
Most of Kai Leng's dialogue also seems to suggest that he's somewhat obsessed with Shepard, wanting to make them recognise him as their ultimate arch-nemesis. Between the Reapers and the Illusive Man, Shepard on the other hand, barely seems to notice Kai Leng at all.
The Scout from Team Fortress 2, at least in the "Meet The Scout" video. He considers it "kind of a big deal" that there's someone who hasn't heard of him.
Murray: ...All right then, 'roll'! Roll through the gates of Hell!... Must you take the fun out of everything?
Lurbuk, an Orc bard from The Elder Scrolls V: Skyrim, is so convinced of his own greatness that he doesn't realize you're there to kill him, even as you draw your blade and tell him he's about to die. As testament to just how bad he is, so many people want him dead that they had to hold a lottery to determine who got to hire the assassin.
Many, many NPCs believe that they are a really big deal in their twelve-man community, but are utterly forgettable to the protagonist. Riverwood, one of the first towns you find, has a bratty kid who will warn you not to get on his bad side. ("Or I'll prank you. And not a little, but a lot.") If you're playing a female, the blacksmith's wife will warn you to stay away from her husband as though he's an incredible catch. Maven Black-Briar technically is a big name since she does rule Riften in all but name, but since she has minimal interaction with the protagonist (one quest, really), she can still come across this when taking the big picture into account. Just walking past her will prompt her to ask if you've come to beg for favors.
Little Buster from Fallout: New Vegas claims to be one of the greatest bounty hunters alive for killing two minor Fiend leaders, even though he's only been doing it for a month. Once the player kills the main three he's inexplicably found dead in the middle of Freeside.
Despite the fire, giant nail, and theme song, Bang Shishigami is said to be the weakest fighter in the entire BlazBlue lineup story-wise. Every time he wins a fight the opponent remarks how lucky he was or how they were stupid for losing to him. You could tell him this to his face all while taking him apart and he will honestly have no clue. However, in a subversion, this only lasts about in the first installment. By the second installment, he's been racking up respects, while still being considered a joke by most of the characters, and it has been revealed that he also has a hidden Nox Nyctores... that he has yet to know how to use, and Word of God says that he will become a very important character in the third installment. Though he goes through something of an emotional blender regarding Litchi and Carl, Bang ends up using his Nox to derail the villains' plans as part of a collective effort by the heroes... until a Diabolus ex Machina kicks in, that is. He also ends up being praised by Azrael, a man who spends his time in Chronophantasmasteamrolling 85% of the cast and only shows the same amount of respect to the likes of Hakumen and Kagura.
Though Chipp may be a double subversion, as while few take him seriously, save for himself, the P.W.A.B.'s analysis highlights him being one of only two remaining users of ki and the only ninja... and then goes on to mention his rash behavior and the ease with which he can be manipulated. A straighter example would be Robo-Ky who, in spite of his ego, is discounted as a threat by both opponents and his own superiors.
Portal's Aperture Science, judging from a slideshow of theirs. The far better-known Black Mesa proposes modest budgets for its projects and is usually given as much. Aperture requests ridiculously large sums of money and usually gets the exact opposite.
This may be more a case of Reed Richards Is Useless or Cut Lex Luthor a Check. Aperture's inventions — all of them — pretty much snap the laws of physics in half and would be unbelievably useful anywhere besides in a pointlessly massive underground deathtrap. The company and Cave Johnson have every right to be insanely proud of their inventions, and Aperture's fiscal problems are most likely excused by Rule of Funny and completely failing to apply those inventions in a more practical manner.
Jolee Bindo from Knightsofthe Old Republic likes to tell a cautionary tale of prophecy and destiny. You see, there was once a man who was told he had a great destiny. This went to his head, and he went around calling himself a great hero. Once, he was caught by a terrible crime lord, and was affronted that the crime lord didn't know who he was. His boasting and threats became so tiresome that the crime boss threw him across the room — and, as it so happens, into a critically fragile part of the ship. The man died, the crime boss died, and Jolee barely escaped with his life. But the destiny was fulfilled - the political and economic structure of the whole sector was never the same afterwards.
Qara in Neverwinter Nights 2 is a vain, arrogant sorceress who loves fire and will kill strangers on a whim or for "practice". Calling her out on this or suggesting that maybe she's not the best thing since sliced bread will result in a temper tantrum and a loss of influence. She's The Scrappy for a reason.
Gene from God Hand was like this before he got the titled God Hand. We're shown how he rescued Olivia from two demons who were going to cut her hand...but he only managed that much because he made a good distraction. His punches did absolutely nothing and he lost one of his arms for the trouble. Oopsie poopsie.
Gromm'ko from World of Warcraft fits. He claims that his raptor, Butcher, can take on anything and anyone.
Likewise a human hunter in an early dwarven area claims to be the greatest hunter on Azeroth (Hemet Nessingway is widely acknowledged as the best) and that the Player Character has likely never even seen the kind of animals he hunts: boars, which are so common most players have killed at least a couple dozen by this point. And will go on to kill a few hundred more.
Galen Trollbane certainly thinks of himself as a hardcore badass with a mighty force at his beck and call. However, he's actually nothing special and the only reason he and his little fiefdom haven't been smacked down is that everyone has more important things to do. When he betrays the Ebon Blade in Legion, Thassarian comes across as more annoyed at having to fight his forces than threatened, despite only having the player character to help.
Torok Bloodtotem boasts of not only the strength of his clan (even after the player has slaughtered their way through them) he also claims that the other tribes and the drogbar are all weaklings, unworthy of living on Highmountain. Notably, the Bloodtotem tribe's only success is in killing some of the Stonedark drogbar who were trading partners with the tauren and thus weren't expecting an attack.
Ryder from Grand Theft Auto: San Andreas talks big and acts like he's "too fucking intelligent" to go to school. While Ryder is a decent shot with a gun, even Sweet tells Ryder that CJ (the player character) has been doing all the work and might be better at being a gangbanger than Ryder is. After you discover Ryder betrayed your gang for a rival gang, he still acts like he's the best. Luckily, you get to put a bullet in his head.
Rufus from Deponia is convinced he's the smartest, coolest and sexiest man on the planet and better than absolutely everyone else he meets. While not completely bereft of talents, he's a scruffy, stuck-up, selfish, clumsy idiotic buffoon.
Handsome Jack in Borderlands2 is an egomaniac full stop. Jack constantly taunts the player characters and the main characters from the first game while bragging about how he killed innocent people because it was hilarious and he has the money to do whatever he wants. Once you kill Jack's daughter, Angel (who begged to be killed because of how she was being used for his plans), Jack goes apeshit and goes on a personal vendetta to kill you while still proclaiming that everything he is doing is for the good of the people of Pandora.
Simon in Soap Opera Dash is convinced that he's all that and a bag of chips, a self-styled "ladies' man" and utterly blind to the fact that the main character has a crush on him. The only thing bigger than his ego might be his hairdo.
Winston Payne is your first prosecutor opponent in nearly every game. He dubs himself as the "Rookie Killer" and claims to be one of the best prosecutors there is. Payne also taunts you every time he gets the upper hand in the trial. Payne easily cracks under pressure and becomes a complete wimp when he starts losing. Payne's brother, Gaspen, is no better and actually runs out of the courthouse like a coward when a witness threatens to bomb the place, even though Phoenix stayed behind and was ready to prove that bomb was fake.
Played straight and later deconstructed and reconstructed with Sebastian Debeste from Investigations 2, who constantly refers to himself as "The Best" prosecutor and generally acts arrogant and dismissive toward his detractors despite his obvious incompetency. It turns out he just wants to impress his father, and the reason he feels so entitled is because he earned a great deal of merits at school in pursuit of this goal. When his father publicly humiliates and denounces him by calling him a useless idiot and revealing that his "successes" are actually the results of favors called in to friends at the school, Sebastian has a breakdown, and it takes Edgeworth convincing him that he's better than his father to get him to dedicate himself to becoming a better prosecutor.
In the intro to Wizard's Work the title character claims to have fought in many wars, placed kings on their thrones and slain numerous enemies while riding on his mighty dragon. The fact that the "mighty dragon" is about as big as a medium-sized dog in actuality and that he gives his age as an obviously-untrue 25 on his employment application makes this highly doubtful.
Eric Sparrow of the Tony Hawk Underground games, especially the first game. He believes that he's pretty much God's gift to skating and when he realizes you're real good, especially after performing a virtually suicidal stunt involving jumping over an active helicopter, he does everything he can to ruin your career.
Jefailey from Divekick, the owner of the Divekick tournament the game takes place in. He decides that just running the tournament doesn't stroke his ego enough, and joins to try and beat it as well. His ego is even incorporated into the gameplay, with his head inflating with each round he wins, increasing his jump height but also making him a bigger target for headshots.
Ognacio Bigglesworth in Without a Clue considers himself the greatest detective in London and that fellow Holmes a mere poser who actually commits the "crimes" he solves.
Raymond Halliday, "adventurer extraordinaire" in Rita James and the Race to Shangri La. He's convinced Rita is hitting on him when she attempts to hire his piloting services and when threatened with violence by some guys he owes money to yells "Not the teeth! I just had them capped!" He also continually refers to himself as "handsome."
Tia from Potion Maker is a mild example. She is a competent potion maker, but tends to overestimate her skills to absurd proportions.
In Batman: Arkham Series the Riddler is intelligent and in later games creates some impressive death traps, but isn't half as smart as he thinks he is. He also frequently refers to himself as Batman's true arch-nemesis, but is a Big Bad Wannabe who Batman and later Catwoman treat as an annoyance.